If the range of t is bounded above and below then there is such apolynomial by the Weierstrass Approximation Theorem. If t is allowed tobe indefinitely large, positive or negative, then there is not for thereason you note.

neenag@cableol.co.uk wrote:

> True or False? :>> There exists a polynomial P such that:>> | P(t) - cos(t) | <= 10^-6.>> |t|, meaning the absolute value of t.>> I said false. Because P(t) could be very large. Then cos(t) is> comparatively small. Then the answer is a large positive number,> greater than 10^-6.>> Although then I started to think along the lines of the Taylor series,> because>> cos(t) = 1 - x^2/2! + x^4/4! - x^6/6! + ...>> and this is valid for all values of t, so perhaps there could be a> polynomial (I'm not sure what that would be).>> So on the other hand it could also be true. Which is the correct> answer?>> Neenag@cableol.co.uk